Question

A bond has a $1,000 par value, 12 years to maturity, and a 8% annual coupon and sells for $980.

What is its yield to maturity (YTM)? Round your answer to two decimal places.

Assume that the yield to maturity remains constant for the next 5 years. What will the price be 5 years from today? Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

(1)-Yield to Maturity [YTM] of the Bond

Yield to Maturity [YTM] = Coupon Amount + [(Par Value – Bond Price) / Maturity Years] / [(Par Value + Bond Price)/2]

Par Value = $1,000

Annual Coupon Amount = $80 [$1,000 x 8%]

Bond Price = $980

Maturity Years = 12 Years

Therefore, Yield to Maturity [YTM] = Coupon Amount + [(Par Value – Bond Price) / Maturity Years] / [(Par Value + Bond Price)/2]

= [$80 + {($1,000 – $980) / 12 Years)] / [($1,000 + $980) / 2]

= [($80 + $1.67) / $990]

= [$81.67 / $980]

= 0.0827

= 8.27%

“Hence, the Yield to Maturity (YTM) of the Bond = 8.27%”

(2)- Price of the Bond 5 years from today

Par Value = $1,000

Annual Coupon Amount = $80 [$1,000 x 8%]

Yield to Maturity (YTM) = 8.27%

Maturity Years = 7 Years [12 Years – 5 Year]

Price of the Bond = Present Value of the Coupon payments + Present Value of Face Value

= $80[PVIFA 8.27%, 7 Years] + $1,000[PVIF 8.27%, 7 Years]

= [$80 x 5.15864] + [$1,000 x 0.57338]

= $412.69 + $573.38

= $986.07

“Therefore, the Price of the Bond 5 years from today would be $986.07”